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SUMMARY:Moments of L-functions and a technique of Sound and Young
DTSTART:20131002T150000
DTEND:20131002T160000
DTSTAMP:20260916T193727Z
UID:5cd3cf165d9df5fc7d7097f7f889131d70e53e7a75f5233ca53d0d5f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ian Petrow (EPFL)\nAbstrait: Let f be a classical holomorphic 
 Hecke cusp form of even weight\, odd level and trivial central character. 
 Consider the family of L-functions given by the quadratic twists L(s\,f \\
 otimes \\chi_K)\, where \\chi_K is the character associated with the quadr
 atic field K.  A classical method to study the these L-functions is to es
 timate the k-th moment of the central values L(1/2\, f \\otimes \\chi_K) o
 r L'(1/2\, f \\otimes \\chi_K) over the family of twists.  Very little is
  know rigorously about this problem\, although random matrix theory provid
 es good conjectures.  When k=1 it is sufficient to use the trace formula 
 (Poisson summation) to obtain an asymptotic estimate\, but already when k=
 2 the trace formula becomes an involution\, and something more is needed.
   I will discuss a technique of Soundararajan and Young to get around thi
 s involutivity and its application (assuming GRH) to obtain asymptotic est
 imates for the 2nd moment of both L(1/2\, f \\otimes \\chi_K) and L'(1/2\,
 f\\otimes \\chi_K).
LOCATION:MA31 http://plan.epfl.ch/?room=MA%20A3%2031
STATUS:CONFIRMED
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